2z-(4-5z)/3z-(8+5z)=3/4

Solution for 2z-(4-5z)/3z-(8+5z)=3/4 equation:

2z-(4-5z)/3z-(8+5z)=3/4

We move all terms to the left:

2z-(4-5z)/3z-(8+5z)-(3/4)=0


Domain of the equation: 3z!=0

z!=0/3

z!=0

z∈R


We add all the numbers together, and all the variables

2z-(-5z+4)/3z-(5z+8)-(+3/4)=0

We get rid of parentheses

2z-(-5z+4)/3z-5z-8-3/4=0

We calculate fractions


2z-5z+(20z-16)/12z+(-9z)/12z-8=0

We add all the numbers together, and all the variables

-3z+(20z-16)/12z+(-9z)/12z-8=0

We multiply all the terms by the denominator


-3z*12z+(20z-16)+(-9z)-8*12z=0

Wy multiply elements

-36z^2+(20z-16)+(-9z)-96z=0

We get rid of parentheses

-36z^2+20z-9z-96z-16=0

We add all the numbers together, and all the variables

-36z^2-85z-16=0

a = -36; b = -85; c = -16;
Δ = b2-4ac
Δ = -852-4·(-36)·(-16)
Δ = 4921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-85)-\sqrt{4921}}{2*-36}=\frac{85-\sqrt{4921}}{-72}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-85)+\sqrt{4921}}{2*-36}=\frac{85+\sqrt{4921}}{-72}
$